An analytical model for the optimization of the laser bending of titanium Ti–6Al–2Sn–4Zr–2Mo

The laser bending of Ti–6Al–2Sn–4Zr–2Mo sheets is analyzed using a well-known conduction model of a traveling Gaussian heat source, which can relate process variables to physical events known to occur at particular temperatures. For instance, incipient melting takes place at specific combinations of the process parameters. Those combinations were derived from dimensionless groups and series of calculations, all conveniently regrouped into empirical expressions. Comparisons of those expressions with observed process parameter combinations for incipient melting allowed the adjustment of the model. After verifying that the derived expressions could predict accurately incipient melting, a similar approach was applied for bending. The model and its derived expressions were used to correlate process variables, temperatures, and measured bending angles. Results of the analysis show that bending was initiated for an estimated surface temperature of 0.48 of the melting temperature. Bending angle was found to attain a maximum at approximately 0.65 of the melting temperature. This corresponds to conditions where the thermal gradients within the thickness and the yielded widths, as calculated from the adjusted model, were both large. By analogy with the empirical expressions for incipient melting, a simple dimensionless equation was derived to help find process parameters to maximize bending angle and therefore assist in the optimization of the process conditions.